Enigma 1423: Around the tree
From New Scientist #2583, 23rd December 2006
We have wrapped all this year’s presents in red or gold and placed them in a circle around the Christmas tree. The set of four anticlockwise starting with Joe’s present is gold, red, red, red. The set of four clockwise which starts with Joe’s present finishes with a red one.
In fact, if you name any sequence of four gold/red (e.g. GRGG, RGGR, etc) then there is a set of four consecutive presents which (clockwise, anticlockwise or both) coincides with your sequence. Furthermore, this would not have been possible with fewer presents.
(a) How many presents were round the tree?
(b) Starting with Joe’s and working clockwise, list the colours of the first five presents.
Enigma 1320 is also called “Around the tree”.